Perturbed Skorohod equations and perturbed reflected diffusion processes

R. A. Doney; T. Zhang

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 1, page 107-121
  • ISSN: 0246-0203

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Doney, R. A., and Zhang, T.. "Perturbed Skorohod equations and perturbed reflected diffusion processes." Annales de l'I.H.P. Probabilités et statistiques 41.1 (2005): 107-121. <http://eudml.org/doc/77834>.

@article{Doney2005,
author = {Doney, R. A., Zhang, T.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Perturbed Skorokhod equations; Local time; Reflection principle; Weak convergence; Reflected diffusions; Stratonovich integration},
language = {eng},
number = {1},
pages = {107-121},
publisher = {Elsevier},
title = {Perturbed Skorohod equations and perturbed reflected diffusion processes},
url = {http://eudml.org/doc/77834},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Doney, R. A.
AU - Zhang, T.
TI - Perturbed Skorohod equations and perturbed reflected diffusion processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 1
SP - 107
EP - 121
LA - eng
KW - Perturbed Skorokhod equations; Local time; Reflection principle; Weak convergence; Reflected diffusions; Stratonovich integration
UR - http://eudml.org/doc/77834
ER -

References

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  1. [1] Ph. Carmona, F. Petit, M. Yor, Some extentions of the arcsine law as (partial) consequences of the scaling property of Brownian motion, Probab. Theory Related Fields100 (1994) 1-29. Zbl0808.60066MR1292188
  2. [2] Ph. Carmona, F. Petit, M. Yor, Beta variables as times spent in [ 0 , ∞ ) by certain perturbed Brownian motions, J. London Math. Soc.58 (1998) 239-256. Zbl0924.60067
  3. [3] L. Chaumont, R.A. Doney, Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion, Probab. Theory Related Fields113 (1999) 519-534. Zbl0945.60082MR1717529
  4. [4] L. Chaumont, R.A. Doney, Some calculations for doubly perturbed Brownian motion, Stochastic Process. Appl.85 (1) (2000) 61-74. Zbl0997.60095MR1730618
  5. [5] B. Davis, Weak limits of perturbed random walks and the equation Y t = B t + α sup s ≤ t Y s + β inf s ≤ t Y s , Ann. Probab.24 (1996) 2007-2023. Zbl0870.60076
  6. [6] B. Davis, Brownian motion and random walk perturbed at extrema, Probab. Theory Related Fields113 (1999) 501-518. Zbl0930.60041MR1717528
  7. [7] R.A. Doney, Some calculations for perturbed Brownian motion, in: Seminaire de Probabilites XXXII, Lecture Notes in Mathematics, 1998, pp. 231-236. Zbl0911.60067MR1655296
  8. [8] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, 1989. Zbl0684.60040MR1011252
  9. [9] J.F. Le Gall, M. Yor, Excursions browniennes et carrés de processus de Bessel, C. R. Acad. Sci. Paris Sér. I303 (1986) 73-76. Zbl0589.60070MR851079
  10. [10] J.F. Le Gall, M. Yor, Enlacements du mouvement brownien autour des courbes de l'espace, Trans. Amer. Math. Soc.317 (1990) 687-7722. Zbl0696.60072MR946219
  11. [11] P.L. Lions, A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math.37 (1984) 511-537. Zbl0598.60060MR745330
  12. [12] M. Perman, W. Werner, Perturbed Brownian motions, Probab. Theory Related Fields108 (1997) 357-383. Zbl0884.60082MR1465164
  13. [13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. Zbl0804.60001MR1303781
  14. [14] W. Werner, Some remarks on perturbed Brownian motion, in: Seminaire de Probabilites XXIX, Lecture Notes in Mathematics, vol. 1613, 1995, pp. 37-43. Zbl0835.60072MR1459447
  15. [15] T.S. Zhang, On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary, Stochastic Process. Appl.50 (1994) 135-147. Zbl0796.60062MR1262335

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